1. Tardigrade
  2. Question
  3. Physics
  4. Acceleration of a particle is given by a=(2+(5 t/2)) m / s 2. At t=0, velocity of the particle is 3 m / s and its position is x=(5/3) m. Find the value of (18/5)((V textavg /V textinst )), where V text avg is average velocity for t=0 to 2 s and V text inst is the instantaneous velocity.at t=2 s.

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Q. Acceleration of a particle is given by $a=\left(2+\frac{5 t}{2}\right) \,m / s ^{2}$. At $t=0$, velocity of the particle is $3 \,m / s$ and its position is $x=\frac{5}{3} m$. Find the value of $\frac{18}{5}\left(\frac{V_{ \text{avg} }}{V_{ \text{inst} }}\right)$, where $V_{\text{ avg }}$ is average velocity for $t=0$ to $2\, s$ and $V_{\text {inst }}$ is the instantaneous velocity.at $t=2\, s$.

Motion in a Straight Line

Solution:

$V=2 t+\frac{5 t^{2}}{4}+3$
$x=t^{2}+\frac{5 t^{3}}{12}+3 t+\frac{5}{3} m / s$
$V_{\text {avg }}=\frac{x(2)-x(0)}{2}=\frac{20}{3} m / s$
$V_{\text {inst }}=V(2)=12 \,m / s$